All Questions
Tagged with sum poisson-distribution
9
questions
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Average of random variables from two Poisson distributions?
I'm lost with a very simple question of finding the average of random variables from two Poisson distributions. I know that if $X\backsim Pois(L1)$ and $Y\backsim Pois(L2)$, then $X+Y\backsim Pois(L1+...
- 145
2
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1
answer
646
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Probability of compound Poisson process
Let $X$ be a compound Poisson process with rate $\lambda$ and increments $Y_i = \pm 1$ with probability $\frac{1}{2}$. Find $P(X(t) = 0)$.
I tried conditioning on $N(t)$:
$$
P(X(t) = 0) = P(\sum\...
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299
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Sum of IID normal variables with index following Poisson distribution
$X_1, X_2,\ldots$ are a sequence of independent normal random variables with mean 1 and variance 1.
Calculate the variance of $X_1+X_2+X_3+\ldots+X_{N+1}$ where $N$ follows Poisson distribution with ...
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2
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457
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Propagation possion errors on scaled count bins
I have a count-channel histogram, where the counts have a standard Poisson uncertainty - if bin $i$ has $C_i$ counts then the uncertainty is $\sqrt{C_i}$.
Now if I were to sum all the bins my job ...
- 190
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685
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Probability of k zeros give the sum of n Poisson random variables is t?
Suppose that I have $X_1,X_2,X_3,...X_n$ iid random variables from a Poisson distribution of parameter $\lambda$. Given that $X_1 +X_2+X_3 +...+X_n = t$, what is the probability that exactly $k$ of $...
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5
votes
1
answer
4k
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Distribution of the sample mean of Poisson random variables
Suppose that you have data x which is modeled as a realization of a Poisson random variable X with expected value $\lambda$>0. I know that the sum of Poisson random variables is also Poisson ...
- 53
1
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44
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Strange error computation
I have statistics question. I have an (astronomical) image, and I want to sum up the pixels within a square, and also get the error of this sum. I use the program DS9 (in case somebody knows it), and ...
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3
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1
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505
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How to find the joint distribution of sums of Poisson random variables
I am trying to determine the joint distribution of two sums of Poisson random variables.
Let's say $X \sim \text{Pois}(\lambda_{1})$, $Y \sim \text{Pois}(\lambda_{2})$, and $Z \sim \text{Pois}(\...
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4
votes
1
answer
169
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Using Poisson distribution to evaluate summations
I'm interested in how to use a Poisson distribution to evaluate $\sum\limits_{x=0}^\infty \frac{(x^2-x+1)(2^x)}{x!}$
I see that this is similar to the general pmf form of $\frac{2^{x}}{x!}$. My ...
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